Typical transform and filter-bank audio coding techniques such as MPEG-1 layers 1 through 3, Dolby AC-3 (also known as Dolby Digital) (Dolby, Dolby Digital and Dolby AC-3 are trademarks of Dolby Laboratories Licensing Corporation), and MPEG-2 Advanced Audio Coding (AAC) reduce transmission data rates by dynamically allocating bits in both time and frequency to remove inaudible redundancies in the audio signal. The dynamic allocation of bits is typically based on signal dependent psychoacoustic principles. Further details of Dolby AC-3 may be found in Digital Audio Compression (AC-3) Standard. Approved Nov. 10, 1994. (Rev 1) Annex A added Apr. 12, 1995. (Rev 2) 13 corrigendum added 24, May 1995. (Rev 3) Annex B and C added 20, Dec. 1995. Further details of AAC may be found in “ISO/IEC MPEG-2 Audio Coding by Bosi et al, presented at the 101st Convention 1996 Nov. 8-11, 1996, Los Angeles, Audio Engineering Society Preprint 4382).
In AAC, bit allocation is achieved using scale factors and global gain parameters contained in the bit stream. The audio spectrum, transformed using a well-known modified discrete cosine transform (MDCT) known as time domain alias cancellation (TDAC) (see Princen et al, “Analysis/synthesis filter bank design based on time domain aliasing cancellation,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-34, pp. 1153-1161, October 1986), is partitioned into bands of approximately half critical bandwidth and the scale factors are applied multiplicatively. The scale factors and global gain jointly represent bit allocation in 1.5 dB steps or approximately quarter bit increments (the exact bit allocation achieved is dependent on the stochastic characteristics of the audio signal and is further complicated by the non-linear quantizer incorporated in AAC). Increasing the scale factor in a band effectively reduces the quantization noise in that band by allocating more bits to that band. Conversely, decrementing a scale factor increases the quantization noise in a particular band by reducing the bits allocated to it.
Because AAC is a forward adaptive audio encoding system, the scale factors are conveyed to the decoder. This is achieved by differentially coding the scale factors and then Huffman coding the differences. The Huffman codes defined in the AAC standard, are such that large variations in the scale factor parameters from band to band lead to excessive consumption of the available bits in the form of side information, which complicates the scale factor derivation as explained in the next section.